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10.1 Sequences and Summation Notation
Objective 1: Find particular terms of a sequence from the general term.
Write the first four terms of each sequence whose general term is given.
an = 4n ‐ 1
a1 = 4(1) – 1 = 4‐1 = 3
a2 = 4(2) – 1 = 8 – 1 = 7
a3 = 4(3) – 1 = 12 – 1 = 11
a4 = 4(4) – 1 = 16 – 1 = 15
The first four terms are 3, 7, 11, and 15
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an = (‐1)n+1 (n + 4)
Objective 2: Use factorial notation.
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Factorials from 0 to 15
Technology
On the TI 83, 84 Calculator: MATH-PRB-#4 is !
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The general term of a sequence is given and involves a factorial. Write the first four terms of each sequence.
an =
(n + 1)!
n2
Evaluate each factorial expression.
18!
16!
20!
2!18!
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(2n + 1)!
(2n)!
Objective 3: Use summation notation.
Technology
On the TI 83, 84 Calculator: 2nd - STAT (list)-MATH-#5 for Sum
2nd - STAT(list)-OPS-#5 for Seq
Then in parenthese type: (expression, X, lower bound, upper bound, increment)
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Find each indicated sum.
6
∑7i
i =1
4
∑ (k − 3)(k + 2)
k =1
6
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7
∑12
i= 3
5
∑
i =1
(i + 2)!
i!
Summation Formulas
n
1.
∑ c=cn
i=1
n
2,
∑i =
i =1
n
3.
∑i
2
i =1
=
n(n + 1)
2
n(n + 1)(2n + 1)
6
n 2 (n + 1) 2
4. ∑ i =
4
i=1
n
3
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Use the summation formulas to evaluate each sum.
20
∑ (i
2
+ 3)
i 1
i=
12
∑7
i 1
i=
30
∑ −18
i=1
24
∑ 4i
i =1
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10
∑ i(i
2
+ 1)
i =1
15
∑ i(i − 1)
2
i =1
9